The day before, gently fry the bacon in a large non-stick frying pan for 30 minutes, until the fat turns golden. Lift on to kitchen paper to absorb excess fat, and leave to cool and crisp. Crumble into pieces and chill.
Put the oil, vinegar and 1⁄2 tsp each salt and freshly ground black pepper into a screw-top jar. Put the lid on securely and shake the dressing, then keep in a cool place (not the fridge or it will go cloudy).
Half an hour ahead, add the tarragon to the dressing, and shake until well mixed. Tip into a bowl and toss with the chicken, radishes and bacon.
Tear the lettuce roughly and arrange on a platter. Snip the cress with scissors and sprinkle over, then top with the chicken.